Maintaining parameter invariance in seemingly unrelated regressions estimation

Abstract

Seemingly unrelated regressions (SUR) is an important estimation methodology in demand analysis. While possessing qualities that make it attractive to applied demand analysts, the SUR estimation technique poses several difficulties, including the lack of parameter invariance in some instances e.g. estimation of consumer demand systems with micro-level data. When data includes zero consumption, corrections used to account for censoring may result in different parameter estimates when different share equations are dropped for estimation. This article proposes an alternative estimation objective which results in invariant parameter estimates when imposing adding-up by dropping equations.

Acknowledgements

The authors gratefully acknowledge the assistance of Dr Octavio Ramirez and participants at the 2005 AAEA conference. Thanks, also, to Alice Boschman for providing the vegetable data. The research was supported in part by the New Mexico Agricultural Experiment Station, Purdue University and the USDA National Needs Fellow Program.

Notes

¹ While Yen and Huang's (2002) approach is not a GLS approach it is included to show the extensive nature of the lack of invariance problem. In addition, an approach analogous to the INSUR approach described in the next section could be developed for maximum likelihood estimations.

² INSUR parameters were estimated using GAMS. For ease of calculation SEs were calculated in GAUSS. Due to rounding errors the two programs produced slightly different SE estimates.